Electronic device protection

ABSTRACT

A method includes permitting a first signal having a first electromagnetic waveform to pass through an apparatus. The method further includes blocking a second signal having a second electromagnetic waveform at the apparatus, wherein the second electromagnetic waveform is different than the first electromagnetic waveform. The apparatus includes a non-conductive substrate and a plurality of cells including conductive members coupled to the non-conductive substrate, where the conductive members are arranged to form a first discontinuous mesh, where regions between the conductive members of the first discontinuous mesh include a phase change material, and where the phase change material undergoes a phase transition from substantially non-conductive to substantially conductive.

CLAIM OF PRIORITY

The present application claims priority from, and is a divisionalapplication of, U.S. patent application Ser. No. 13/303,416, filed Nov.23, 2011, which is a continuation-in-part of U.S. patent applicationSer. No. 12/857,413 (now issued as U.S. Pat. No. 8,325,495), filed Aug.16, 2010, the contents of each of which are incorporated by referenceherein in their entirety.

FIELD OF THE DISCLOSURE

The present disclosure is generally related to apparatus, systems andmethods for electronic device protection.

BACKGROUND

Low-noise amplifiers in antennas and direction arrival estimationsystems may be susceptible to high-power microwave attacks orinterference from other devices located near the low-noise amplifiers.In phased array antenna systems and certain other communication systems,silicon carbide (SiC)-based limiters may be placed in-line to provideprotection against high-power signals. For example, the SiC-basedlimiters may be placed between an antenna and the low-noise amplifiersto reduce the amount of power that goes through the low-noiseamplifiers. The SiC-based limiters may be integrated at each element ofa phased array antenna. Since phased array antennas may includethousands of elements, placing limiters at each element may introducesignificant costs and complexity.

Another method of protecting electronic devices, such as low-noiseamplifiers, from exposure to high-power electromagnetic radiation, e.g.,high-power microwave radiation, may be to place a switchabletransistorized mesh system in front of an antenna array. The switchabletransistorized mesh system may include conductors arranged in a meshwith discontinuities. A transistor may be present at each discontinuity.When the transistors are off (e.g., behaving like an open switch),electromagnetic energy may pass through the mesh. When the transistorsare on (e.g., behaving like a closed switch), the mesh is effectivelycontinuous, and electromagnetic energy may be reflected from the mesh.Since each transistor is provided with power for switching, significantcomplexity may be added by using such a switchable transistorized meshsystem. Further, switching time of the transistors may add anunacceptable delay.

SUMMARY

Apparatus, systems and methods for electronic device protection areprovided. A particular apparatus includes a non-conductive substrate anda plurality of cells including conductive members coupled to thenon-conductive substrate. The conductive members are arranged to form afirst discontinuous mesh. Regions between the conductive members of thefirst discontinuous mesh include a phase change material. The phasechange material undergoes a phase transition from substantiallynon-conductive to substantially conductive responsive to a change ofenergy.

A particular system includes an electronic device and a protectionapparatus to protect the electronic device by selectively blockingelectromagnetic radiation. The protective apparatus includes anon-conductive substrate and a plurality of cells including conductivemembers coupled to the non-conductive substrate. The conductive membersare arranged to form a first discontinuous mesh. Regions between theconductive members of the first discontinuous mesh include a phasechange material. The phase change material undergoes a phase transitionfrom substantially non-conductive to substantially conductive responsiveto a first electromagnetic waveform.

A particular method includes permitting a first signal having a firstelectromagnetic waveform to pass through an apparatus and blocking asecond signal having a second electromagnetic waveform at the apparatus.The second electromagnetic waveform is different than the firstelectromagnetic waveform. The apparatus includes a non-conductivesubstrate, a discontinuous mesh of conductive members, and a phasechange material disposed between the conductive members of thediscontinuous mesh. The phase change material undergoes a phasetransition from substantially non-conductive to substantially conductiveat least partially responsive to the second electromagnetic waveform.

The features, functions, and advantages that have been described can beachieved independently in various embodiments or may be combined in yetother embodiments, further details of which are disclosed with referenceto the following description and drawings, which are not to scale.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a plan view of a particular embodiment of an apparatus toprotect an electronic device;

FIG. 1B is a view of a particular portion of the apparatus of FIG. 1A;

FIG. 2A is a sectional view of a gap between cells of a first embodimentof the apparatus of FIG. 1A in a first operational state;

FIG. 2B is a sectional view of a gap between cells of the firstembodiment of the apparatus of FIG. 1A in a second operational state;

FIG. 3A is a sectional view of a gap between cells of a secondembodiment of the apparatus of FIG. 1A in a first operational state;

FIG. 3B is a sectional view of a gap between cells of the secondembodiment of the apparatus of FIG. 1A in a second operational state;

FIG. 4A is a perspective view of a first particular embodiment of asystem to protect an electronic device in a first operational state;

FIG. 4B is a perspective view of the system of FIG. 4A in a secondoperational state;

FIG. 5 is a perspective view of a second particular embodiment of asystem to protect an electronic device;

FIG. 6 is a flow chart of a first particular embodiment of a method toprotect an electronic device;

FIG. 7 is a flow chart of a second particular embodiment of a method toprotect an electronic device;

FIG. 8 is a graph of simulated scattering parameters of a particularembodiment of a protection device in a first operational state;

FIG. 9 is a graph of simulated scattering parameters of a particularembodiment of a protection device in a second operational state;

FIG. 10 is a graph of simulated electric field characteristics acrosshalf of a gap of a discontinuous mesh according to a first particularembodiment;

FIG. 11 is a graph of simulated electric field characteristics acrosshalf of a gap of a discontinuous mesh according to a second particularembodiment;

FIG. 12 is a graph of simulated electric field characteristics acrosshalf of a gap of a discontinuous mesh according to a third particularembodiment; and

FIG. 13 is a graph of estimated turn on time of a protection deviceaccording to a particular embodiment.

DETAILED DESCRIPTION

Embodiments disclosed herein include an inexpensive low-loss,wide-bandwidth, radio frequency (RF) shutter for use in protectingelectronic devices, such as low-noise amplifiers and other communicationsystems. The RF shutter may include conductive elements arranged in amesh. The conductive elements of the mesh may have a plurality ofintersections. The conductive elements may be separated by a gap or aphase change material. For example, an area between the conductiveelements may include discontinuities formed by a phase change materialor phase change materials. The phase change material may besubstantially non-conductive in a first phase and substantiallyconductive in a second phase. As used herein, a substantiallynon-conductive material refers to a material that has few mobile chargecarriers, such as an insulator or dielectric. Thus, a substantiallynon-conductive material has a high dielectric constant. In contrast, asubstantially conductive material herein refers to a material with anabundance of moveable charge carriers, such as a metal or plasma. Toillustrate, the phase change material may be a material such as vanadiumdioxide, which undergoes a metal-insulator phase transition. In anotherexample, the phase change material may be a gas that undergoes agas-to-plasma phase transition. The phase transition from the firstphase to the second phase may be triggered responsive to particularelectromagnetic waveforms.

The discontinuities between the conductive elements enable thediscontinuous mesh to be transparent to certain electromagnetic waves(e.g., relatively low-power, low-frequency signals). However, in thepresence of other electromagnetic waves (e.g., relatively high-power orhigh-frequency signals), the phase change material in thediscontinuities may become conductive. For example, a gas in microgapsbetween the conductive elements may form a plasma. The plasma isconductive and electrically bridges the microgap causing the mesh tobehave as a continuous mesh and to reflect the electromagnetic waves. Inanother example, an insulator-metal phase change material between theconductive elements may undergo a phase transition from an insulator(i.e., substantially nonconductive) phase to a metal (i.e.,substantially conductive) phase, thereby electrically bridging theconductive elements.

In a particular embodiment, when a plasma is formed between theconductive elements, the plasma may be a cold plasma. A cold plasma maybe only partially ionized. For example, in a cold plasma as little asabout 1% of a gas may be ionized. This is in contrast to a thermal orhot plasma, in which a much higher proportion of the gas may be ionized.When an insulator-metal phase change material is used, theinsulator-metal phase change material may include a dopant or othermaterial that changes phase transition properties of the insulator-metalphase change material. For example, a dopant may be added to adjustconditions at which the insulator-metal phase change material undergoesthe phase transition.

Electronic devices protected by the RF shutter may retain normaloperation (e.g., transmission and reception of relatively low-power,low-frequency signals) during periods between exposures to relativelyhigh-power or high-frequency signals. However, during exposure to thehigh-power or high-frequency signals, the RF shutter may respond quicklyand with little complexity to protect the electronic devices. Toillustrate, when a high-power or high-frequency signal is received atthe RF shutter, a large electric field may be generated in eachmicrogap. The electric field may be sufficient to form an atmosphericpressure plasma or to initiate a phase transition in a phase changematerial, causing the mesh to behave as a continuous mesh. Thus, themesh may act like a ground plane and reflect the high-power orhigh-frequency signal to protect the electronics behind it. Accordingly,a passive RF shutter can protect electronics from high-power andhigh-frequency signals when in an “on” state and allow transmission andreception of lower power, lower frequency signals when in an “off”state. A power level and a frequency of an incoming signal may determinewhether the RF shutter is on or off.

FIG. 1A is a plan view of a particular embodiment of an apparatus 100 toprotect an electronic device, and FIG. 1B is a closer view of aparticular portion of the apparatus 100. The apparatus 100 includes anon-conductive substrate 102 and a plurality of conductive members 106.The conductive members 106 are arranged to form a discontinuous mesh104. For example, the conductive members 106 may be arranged in cells,two of which are illustrated in FIG. 1B, with a gap 110 between adjacentcells. For example as shown in FIG. 1B, two cells including conductivemembers 106 and 107 are separated by the gap 110. Each of the cells hasa characteristic dimension 114, such as width from center to center ofadjacent gaps or a width from center to center of the conductive members106 and 107. In a particular embodiment, the cells are approximatelysquare and the characteristic dimension 114 is selected based on a firstwavelength of a first signal to be allowed to pass through the apparatus100 and a second wavelength of a second signal that is to be blocked bythe apparatus 100. For example, the characteristic dimension 114 may bemuch smaller than the first wavelength, e.g., approximately onetwenty-fifth of the first wavelength. In another example, thecharacteristic dimension 114 may be smaller than but closer to thesecond wavelength, e.g., approximately one half of the secondwavelength. However, other proportions between the characteristicdimension 114 and the wavelength of the first signal and the secondsignal may also be used.

A width of the gaps 110 is related to electric field strength present inthe gap 110 when the conductive elements 106 and 107 are subjected toelectromagnetic radiation. For a particular frequency of electromagneticradiation, a smaller gap width leads to a stronger electric field in thegap 110 and a larger gap width provides a weaker electric field in thegap 110.

The non-conductive substrate 102 may include a ceramic material, apolymer material, or another material that is not conductive or isdielectric. The non-conductive substrate 102 may be substantiallytransparent to electromagnetic energy in a particular range of concern.For example, the non-conductive substrate 102 may be transparent to awavelength of signals intended to be transmitted and received throughthe apparatus 100 (e.g., relatively low-power, relatively low-frequencysignals). The non-conductive substrate 102 may also be substantiallytransparent to signals to be blocked from transmissions through theapparatus 100 (e.g., relatively high-power or relatively high-frequencysignals). The non-conductive substrate 102 may have a thicknesssufficient to provide desired structural stability. In a particularembodiment, the non-conductive substrate 102 may be formed of a materialthat facilitates removal of heat that may be built up by the apparatus100 during use. For example, the non-conductive substrate 102 may beformed of aluminum nitride, which is electrically insulating but mayhave suitable thermal conductivity.

The conductive members 106 and 107 may include any suitable conductor,such as silver, gold, copper, aluminum, or another metal or conductorselected for a particular application. In a particular embodiment,materials used to form the non-conductive substrate 102 and theconductive members 106 and 107 may be selected to facilitate low costmanufacturing of the apparatus 100. For example, the materials may beselected to facilitate manufacturing of the apparatus 100 usingrelatively inexpensive fabrication techniques that are commonly employedto manufacture integrated circuits and other electronic devices. Toillustrate, the materials may be selected to enable manufacturing theapparatus 100 using wet etch, dry etch, deposition, photolithography,imprint lithography, chemical mechanical polishing, printing, or otheradditive or subtractive processes that are used to manufactureelectronics and integrated circuits. For purposes of simulationsdescribed below the conductive members 106 and 107 were simulated to beformed of copper. The conductive members 106 and 107 may have athickness of as little as a few skin depths. For example, for copperconductive members the skin depth may be approximately 3 microns, so athickness of several skin depths, e.g., about 10 microns, may besufficient.

In a particular embodiment, a phase change material 112 may be presentat each of the gaps 110. For example, as described with reference toFIGS. 2A and 2B, the phase change material 112 may include a gas thatundergoes a phase transition to a plasma. In another example, asdescribed with reference to FIGS. 3A and 3B, the phase change material112 may include a material that undergoes an insulator-metal phasetransition, such as vanadium dioxide. The phase change material 112 mayundergo a phase transition from a substantially non-conductive phase toa substantially conductive phase at least partially responsive to anincident electromagnetic waveform at the apparatus 100. Thus, thediscontinuous mesh 104 may act as a continuous mesh responsive to theincident electromagnetic waveform. Accordingly, the apparatus 100 mayselectively inhibit transmission of electromagnetic radiation based, forexample, on characteristics of the electromagnetic radiation.

FIG. 2A is a sectional side view of a gap 110 between cells of a firstembodiment of the apparatus 100 of FIG. 1A in a first operational state.FIG. 2B is a sectional side view of the gap 110 between the cells of thefirst embodiment of the apparatus 100 of FIG. 1A in a second operationalstate. As illustrated in FIG. 2A, a first signal having a first waveform120 may be received at the apparatus 100 and may be transmitted orpermitted to propagate through the apparatus 100. Referring to FIG. 2B,a second signal having a second waveform 122 may be received at theapparatus 100 and may cause a gas (e.g., the phase change material 112in the embodiment of FIG. 2A) in a cavity 116 defined proximate the gap110 to form a plasma 130. The plasma 130 provides a conductive pathacross the gap 110. The plasma 130 may be electrically conductive enoughto bridge the gap 110 to cause the discontinuous mesh formed by theconductive members 106 and 107 to behave as a continuous mesh. Forexample, electron density in the gap 110 may range from about 10̂13electrons per cubic centimeter to as much as 10̂17 electrons per cubiccentimeter, with a conductivity measuring from about 10̂2 Siemens permeter (S/m) to about 10̂4 S/m. Thus, the second signal having the secondwaveform 122 stimulates formation of the plasma 130 and thereby causesthe discontinuous mesh to be continuous, blocking or inhibitingtransmission or propagation of the second signal.

In the embodiment of FIGS. 2A and 2B, the cavity 116 may be formed inthe non-conductive substrate 102 at the gap 110 between the adjacentconductive members 106 and 107. The cavity 116 may undercut a portion ofthe adjacent conductive members 106 and 107. The cavity 116 may have adepth of a same order of magnitude as the width of the gap 110. Forexample, when the width of the gap 110 is about 20 μm, the cavity 116may have a depth of about 10 μm to about 40 μm. The cavity 116 mayinclude the gas that forms the plasma 130 when the gas is excited byparticular electromagnetic waveforms.

In a particular embodiment, the gas is retained by an overlayingsubstrate 103. In yet another embodiment, the overlaying substrate 103may be large enough to encapsulate the whole mesh array rather than atindividual gap 110 areas. The overlaying substrate 103 may be formed ofthe same material as the non-conductive substrate 102. For example, theconductive members 106 and 107 may be substantially encased or embeddedwithin the non-conductive substrate 102 and the overlaying substrate103. In another particular embodiment, the overlaying substrate 103 maynot be present. For example, an upper surface 108 of the apparatus 100may be exposed to air, and the air may form the plasma 130. In anotherexample, the upper surface 108 of the apparatus 100 may be covered toretain the gas that forms the plasma 130. The gas may include air, anoble gas (e.g., argon), or another gas that has an acceptable operatingrange between an electric field strength that causes the gas to generatethe plasma 130 and an electric field strength that causes dielectricbreakdown of the gas, as described further below. For example, thedielectric breakdown field strength for air is about 60 times the plasmageneration field strength, providing a dynamic operating range of about18 decibels.

The apparatus 100 may selectively inhibit transmission ofelectromagnetic radiation based on characteristics of theelectromagnetic radiation. For example, the gas may form the plasma 130that electrically bridges the gap 110 to form an electrically continuousmesh in response to electromagnetic radiation having firstcharacteristics (e.g., the second waveform 122). When the plasma 130electrically bridges the gaps, the electromagnetic radiation having thefirst characteristics is inhibited from passing through the apparatus100. However, the apparatus 100 allows electromagnetic radiation thathas second characteristics (e.g., the first waveform 120) to passthrough the apparatus 100.

FIG. 3A is a sectional side view of a gap 110 between cells of a secondembodiment of the apparatus 100 of FIG. 1A in a first operational state.FIG. 3B is a sectional side view of the gap 110 between the cells of thesecond embodiment of the apparatus 100 of FIG. 1A in a secondoperational state. As illustrated in FIG. 3A, in the first operationalstate, the phase change material 112 is in a substantiallynon-conductive phase, and a first signal having a first waveform 120 maybe received at the apparatus 100 and may be transmitted or permitted topropagate through the apparatus 100. Referring to FIG. 3B, a secondsignal having a second waveform 122 may be received at the apparatus 100and may cause the apparatus 100 to transition to the second operationstate. For example, the second waveform 122 may cause the phase changematerial 112 to undergo a phase transition to a substantially conductivestate. In the substantially conductive state, the phase change material112 provides a conductive path across the gap 110. Thus, in thesubstantially conductive state, the phase change material 112 causes thediscontinuous mesh to become continuous, blocking or inhibitingtransmission or propagation of the second signal.

In the embodiment of FIGS. 3A and 3B, the phase change material 112 mayinclude any material that undergoes a solid-solid metal-insulator phasetransition. Such solid-solid metal-insulator phase transitions are alsoreferred to in the art as semiconductor-metal phase transitions.Examples of such materials that undergo a solid-solid metal-insulatorphase transition include, but are not limited to, GeSb₂Te₄, RNiO₃ (whereR=Pr, Nd, or Sm), LaCoO₃, particular transition metal oxides, such ascertain titanium oxides, e.g., titanium sequioxide (Ti₂O₃), certainvanadium oxides, e.g., vanadium dioxide (VO₂), and vanadium sequioxide(V₂O₃). The phase change material 112 may also be doped with anothermaterial to modify characteristics of the phase transition, such as aphase transition critical temperature or another critical property atwhich the phase transition occurs (e.g., electric field strength,current, voltage, etc.). Dopants may include, for example, W, Cr, Ta, Alor another material.

The apparatus 100 may selectively inhibit transmission ofelectromagnetic radiation based on characteristics of theelectromagnetic radiation. For example, the phase change material 112may undergo the phase transition responsive, at least partially, to thecharacteristics of the electromagnetic radiation. That is, thecharacteristics of the electromagnetic radiation alone or in concertwith other factors (e.g., a temperature of the apparatus 100, a biascurrent applied to the apparatus 100, another signal applied to theapparatus 100, or another factor that preconditions or biases the phasechange material 112 to be near a phase transition critical point) maycause the phase change material 112 to undergo the phase transition. Toillustrate, the first waveform 120 may have first characteristics (e.g.,frequency, power, electric field generated in the gap 110) that do notcause the phase change material 112 to undergo the phase transition, andthe second waveform 122 may have second characteristics (e.g.,frequency, power, electric field generated in the gap 110) that causethe phase change material 112 to undergo the phase transition.

FIG. 4A is a perspective view of a first particular embodiment of asystem to protect an electronic device in a first operational state. Thesystem includes an electronic device 404 coupled to an antenna 402 andprotected by the apparatus 100. The electronic device 404 may includeone or more low-noise amplifiers or other devices to be protected fromhigh-power or high-frequency signals.

A first signal having a first waveform 420 may be transmitted by atransmitter 406 and received at the antenna 402. The first waveform 420may have characteristics (such as a wavelength 408) that do not cause aphase change material present in gaps of the apparatus 100 to undergo aphase transition. Thus, the first signal is able to pass through theapparatus 100, to be received at the antenna 402, and to be sent as asignal 410 to the electronic device 404.

FIG. 4B is a perspective view of the system of FIG. 4A in a secondoperational state. In FIG. 4B, the transmitter 406 transmits a secondsignal having a second waveform 432. The second waveform 432 may becharacterized by particular parameters, such as a second wavelength 430,an amplitude, a signal strength, and so forth. When the second signal isreceived at the apparatus 100, the second signal may stimulate the phasechange material of the apparatus 100 to undergo the phase transition.Accordingly, the apparatus 100 in FIG. 4B is illustrated as continuous(i.e., without gaps) due to the presence of the substantially conductivephase of the phase change material in the gaps of the apparatus 100. Theapparatus 100 may act as a ground plane to reflect or block transmissionof the second signal, resulting in the second signal not being receivedat the antenna 402. As illustrated in FIG. 4B, no second signal 434 isreceived at the electronic device 404, and the electronic device 404 isprotected from harm as a result of the second signal.

Thus, the apparatus 100 acts as a passive RF shutter to that allows somesignals to pass through and blocks or reflects other signals. Putanother way, the apparatus 100 has a first operational state in whichthe apparatus 100 is substantially transparent to a firstelectromagnetic waveform and a second operational state that is engagedwhen the apparatus 100 is exposed to a second electromagnetic waveformthat is different than the first electromagnetic waveform. In the secondoperational state, the apparatus 100 may be substantially opaque to thefirst electromagnetic waveform and to the second electromagneticwaveform. The apparatus 100 is able to block certain signals quickly,with little added complexity, and without the use of external controlsystems and power systems. Rather, the signal to be blocked itselfstimulates the phase transition that causes the signal to be blocked.Accordingly, the switching time required to switch the apparatus 100from the first operational state (where signals are allowed to passthrough) to the second operational state (where signals are not allowedto pass through) may be less than about 2 nanoseconds. In someembodiments, the switching time may be less than a nanosecond. Forexample, the switching time when a solid-solid phase change material isused may be less than one picoseconds, e.g., about 100 femtoseconds.

FIG. 5 is a perspective view of a second particular embodiment of asystem to protect the electronic device 404. The system of FIG. 5 is anactive protection system for the electronic device 404. The systemincludes a third transmitter 526 that sends a third signal having athird waveform 522. The third waveform 522 may include particularcharacteristics, such as a third wavelength 524, an amplitude, andsignal strength when received at the apparatus 100. As previouslydescribed, the apparatus 100 is discontinuous and substantiallytransparent to signals having certain waveforms, which enables thosesignals to be received at the antenna 402. In a particular embodiment,the third waveform 522 is selected to stimulate the phase transition inthe phase change material present in the gaps of the apparatus 100. Forexample, the third transmitter 526 may be a relatively low power, highfrequency transmitter located relatively near the antenna 402.

In a particular embodiment, the third transmitter 526 is under controlof a controller 540 associated with the electronic device 404. The thirdtransmitter 526 may be used to turn on protective characteristics of theapparatus 100 in response to the controller 540. For example, thetransmitter 406 may be a perceived threat to the electronic device 404.That is, the transmitter 406 may be capable of transmitting a fourthsignal 520 that may be harmful to the electronic device 404. Thecontroller 540 may engage the third transmitter 526 to stimulate thephase transition of the phase change material of the apparatus 100 whenthe perceived threat is near the electronic device 404.

In another example, the transmitter 406 may be a relatively high-powertransmitter that is collocated with the electronic device 404. Thetransmitter 406 may periodically or occasionally transmit signals thatcould be harmful to the electronic device 404. The controller 540 mayselectively engage the third transmitter 526 to stimulate the phasetransition of the phase change material of the apparatus 100 when thetransmitter 406 is transmitting or is about to transmit the potentiallyharmful fourth signal 520.

In yet another example, the third transmitter 526 may send the thirdsignal to stimulate the phase transition of the phase change materialall of the time except for when the electronic device 404 is to send orreceive signals via the antenna 402. To illustrate, the thirdtransmitter 526 may leave the apparatus 100 “on” (e.g., in the secondoperational state described above) to block signals from being receivedat the electronic device 404 until a particular time when the signalsare expected or desired, at which point the third transmitter 526 maycease sending the third signal to turn the apparatus 100 “off” (e.g., inthe first operational state described above).

In a particular embodiment, the system includes the first apparatus 100and a second apparatus 550. The second apparatus 550 may be included asa layer over or under the first apparatus 100. The second apparatus 550may include a second discontinuous mesh formed by second conductivemembers spaced apart by second gaps. The second apparatus 550 may beconfigured to transition from the first operational state, in which themesh of the second apparatus 550 is discontinuous, to the secondoperation state, in which the mesh of the second apparatus 550 behavesas continuous, in a different manner than or responsive to differentconditions than the first apparatus 100. For example, the second gapsmay have different widths than the gaps of the apparatus 100. The widthof the gap may be related to the electric field strength in the gap whena mesh is exposed to electromagnetic radiation. Thus, smaller gaps mayexhibit a stronger electric field than larger gaps. Accordingly, thelarger gaps of the second apparatus 550 may experience smaller electricfields than the smaller gaps of the first apparatus 100 when both aresubjected to the fourth signal 520. Thus, a phase change that isresponsive to electric field strength may occur under differentcircumstance in the second apparatus 550 than at the first apparatus100. To illustrate, a higher power signal or higher frequency signal maycause the phase transition of the second apparatus 550 than a signalthat causes the phase transition of the first apparatus 100. A very highpower signal may cause failure of the first apparatus 100, e.g., byexceeding a dielectric breakdown threshold of the phase change material.In this circumstance, the second apparatus 550 provides a higher powertolerance backup to the first apparatus 100, while the first apparatus100 provides lower power switching to the second operational state(e.g., “on” state) to provide a fast switching response to the fourthsignal 520.

To illustrate, when the phase change material is a gas that undergoes aphase transition to a plasma and when the fourth signal 620 is arelatively high-power signal, the smaller gaps of the apparatus 100 mayhave a strong enough electric field to exceed a dielectric breakdownthreshold of the gas in the gaps of the apparatus 100. Thus, the gaps ofthe apparatus 100 may experience damaging arching or coronal discharge.The second gaps of the second apparatus 550 are larger and have asmaller electric field. When the apparatus 100 and the second apparatus550 use the same gas in their respective gaps, the second gaps canendure a stronger signal than the gaps of the apparatus 100 withoutexceeding the dielectric breakdown threshold of the gas. In a particularembodiment, the apparatus 100 and the second apparatus 550 may usedifferent gases with different dielectric breakdown threshold to provideprotection against signals with different signal strengths.

In another example, the first apparatus 100 may include a firstmetal-insulator phase change material and the second apparatus 550 mayinclude a second metal-insulator phase change material. The firstmetal-insulator phase change material may undergo a phase transitionunder different circumstances than the second metal-insulator phasechange material. Thus, the first metal-insulator phase change materialand the second metal-insulator phase change material may be responsiveto different signal characteristics and thus provide protection againstdifferent signals. Alternately, or in addition, the firstmetal-insulator phase change material may fail (e.g., due to resistiveheating) under different circumstances than the second metal-insulatorphase change material. Thus, the second apparatus 550 may be a backup tothe first apparatus 100.

In yet another example, the phase change materials used in each of theapparatuses 100, 550 are of different types. To illustrate, the firstapparatus 100 may include a metal-insulator phase change material, andthe second apparatus 550 may include a gas that undergoes a phasetransition to a plasma. Alternately, the second apparatus 550 mayinclude the metal-insulator phase change material, and the firstapparatus 100 may include the gas that undergoes the phase transition tothe plasma. The particular types of the phase change materials of eachapparatus 100, 550 and the arrangement of the apparatuses 100, 550 maybe selected based on protective characteristics that are desired for thesystem. For example, since the solid-solid metal-insulator phasetransition is generally faster than a gas-plasma phase transition, thefirst apparatus 100 may use a solid-solid metal-insulator phase changematerial to provide a rapid response solid-solid metal-insulator phasechange material that may break down at a lower power level than a plasmagenerated in relatively large gaps of the second apparatus 550.Accordingly, a gas-plasma material may be used with the relatively largegaps in the second apparatus 550.

Gaps widths, characteristic dimensions, phase change materials (e.g.,gases, dopants, etc.), or any combination thereof of the apparatus 100and the second apparatus 550 may be selected to cause the apparatus 100and the second apparatus 550 to provide different protectioncharacteristics. For example, the second apparatus 550 may have adifferent characteristic dimension than the characteristic dimension 114(shown in FIG. 1) of the first apparatus 100. Thus, the first apparatus100 and the second apparatus 550 may turn on (e.g., transition to thesecond operational state) in response to different waveforms and may beable to endure different waveforms without being overpowered (e.g.,before a dielectric breakdown threshold is reached). In another example,when both of the apparatuses 100, 550 use metal-insulator phase changematerials in the gaps, the gaps of the apparatuses 100, 550 may be thesame size and the metal-insulator phase change materials may bedifferent to provide different response characteristics of theapparatuses 100, 550. To illustrate, the first metal-insulator phasechange material may be doped, and the second metal-insulator phasechange material may be undoped or differently doped to provide responsecharacteristics that are distinct from response characteristics of thefirst metal-insulator phase change material.

Further, although only two apparatuses are illustrated in FIG. 5, thesystem may include more than two apparatuses or layers. When more thantwo apparatuses are included, the additional apparatus or apparatusesmay have characteristic dimensions, phase change materials (e.g., gases,dopants, etc.) and/or gaps selected to provide desired protectioncharacteristics. Additionally, although the second apparatus 550 is onlyshown in the active system illustrated in FIG. 5, the second apparatus550 or other layers may be used with a passive system, such as thesystem described with reference to FIGS. 4A and 4B.

FIG. 6 illustrates a first particular embodiment of a method ofprotecting an electronic device. The method includes, at 602, permittinga first signal having a first electromagnetic waveform to pass throughan apparatus. For example, the apparatus may be a protection device,such as the apparatus 100 of FIG. 1, that includes a non-conductivesubstrate and a discontinuous mesh of conductive members. A phase changematerial may be disposed between the conductive members of thediscontinuous mesh. The phase change material may undergo a phasetransition from substantially non-conductive to substantially conductiveat least partially responsive to the second electromagnetic waveform.For example, the phase transition may include a solid-solidmetal-insulator phase transition, a gas-plasma phase transition, oranother phase transition that results in a non-conductive tosubstantially conductive material becoming conductive.

The method also includes, at 604, blocking a second signal having asecond electromagnetic waveform at the apparatus. The secondelectromagnetic waveform may be different than the first electromagneticwaveform. The second electromagnetic waveform may cause the phase changematerial to undergo the phase transition and to become substantiallyconductive. For example, a wavelength of the second electromagneticwaveform may be smaller than a wavelength of the first electromagneticwaveform, at 606. The phase change material may undergo the phasetransition responsive, at least in part, to effects of the wavelength ofthe second electromagnetic waveform on the apparatus or on the phasechange material. In another example, a power of the second signal may begreater than the first signal, at 608. The phase change material mayundergo the phase transition responsive, at least in part, to effects ofthe power of the second electromagnetic waveform.

The method may also include, at 610, applying an activation signal tothe apparatus to cause the second signal to be blocked. For example, atransmitter, such as the third transmitter 526 of FIG. 5, may be used toselectively turn the apparatus “on,” so that signals are blocked, or“off,” so that signals can pass through. In a particular embodiment, theactivation signal may have a first polarization and an incoming signalmay have a second polarization that is different from the firstpolarization. The incoming signal may be blocked based on firstpolarization of the activation signal, at 612.

FIG. 7 illustrates a second particular embodiment of a method ofprotecting an electronic device. The method includes, at 702, permittinga first signal having a first electromagnetic waveform to pass throughan apparatus. For example, the apparatus may be a protection device,such as the apparatus 100, that includes a discontinuous mesh ofconductive members separated by gaps. The apparatus may include anon-conductive substrate and a plurality of cells including conductivemembers. Conductive members may be arranged to form the discontinuousmesh. Each conductive member of a cell is separated from conductivemembers of adjacent cells by a gap. A cavity may be defined in thenon-conductive substrate at each gap. In response to exposure toparticular electromagnetic waveforms, a plasma may be formed in thecavity at each gap.

The method also includes, at 704, blocking a second signal having asecond electromagnetic waveform at the apparatus. The secondelectromagnetic waveform may be different than the first electromagneticwaveform. For example, the second electromagnetic waveform may cause amaterial present in the cavity at each gap to be ionized to form aplasma, at 706. To illustrate, a wavelength of the secondelectromagnetic waveform may be smaller than a wavelength of the firstelectromagnetic waveform, at 708. The wavelength of the secondelectromagnetic waveform may stimulate or excite the material present inthe cavity to form the plasma. In another illustrative example, thepower of the second signal may be greater than the first signal, at 710.The plasma may be stimulated in the cavity at each gap in response tothe second signal due to the signal strength.

The method may also include, at 712, applying an activation signal tothe apparatus to cause the second signal to be blocked. For example, atransmitter, such as the third transmitter 526 of FIG. 5, may be used toselectively turn the apparatus “on,” so that signals are blocked, or“off,” so that signals can pass through. In a particular embodiment, theactivation signal may have a first polarization and an incoming signalmay have a second polarization that is different from the firstpolarization. The incoming signal may be blocked based on firstpolarization of the activation signal, at 714.

FIGS. 8-13 illustrate results of simulations that were conducted tocharacterize performance of a protection device, such as the apparatus100 described above. For purposes of the simulations, the conductivemembers 106 and 107 of the apparatus 100 were simulated as 70 μm widecopper traces with gaps midway between intersections of vertical andhorizontal traces. For a first simulation, results of which areillustrated in FIGS. 8, 9, 10 and 12, the gaps 110 were simulated ashaving a width of approximately 20 μm, and the cell size orcharacteristic dimension 114 of the cells was simulated as about 5 mm.For a second simulation, results of which are illustrated in FIG. 11,the gaps 110 were simulated as having a width of approximately 80 μm,and the cell size or characteristic dimension 114 of the cells wassimulated as about 5 mm.

FIG. 8 is a graph of scattering parameters of a simulated protectiondevice in a first operational state in which the gaps arediscontinuities in the conductive members. As shown in FIG. 8, whensubjected to a 2.45 gigahertz signal, substantially all of the signal istransmitted through the apparatus, with less than a 30 decibelreflection at 2.45 gigahertz.

FIG. 9 is a graph of simulated scattering parameters of a particularembodiment of a protection device in a second operational state in whichno discontinuities are present in the conductive members. FIG. 9 showsthat with the gaps bridged, the apparatus 100 acts as an effectiveground plane and reflects most of the incoming signal with less than 12decimals getting through at 2.45 gigahertz. It is noted that performanceof the apparatus 100 may be improved by adjusting a size of the mesh(e.g., a distance between intersection points or approximate size of thecells) to be more sub-wavelength. The performance of the apparatus 100may also be improved by using several layers of mesh with differentcharacteristics.

FIG. 10 is a graph of simulated electric field characteristics acrosshalf of a gap of a discontinuous mesh according to a first particularembodiment. Magnitude of the electric field is shown along the y-axis. Alocation along the gap is shown along the x-axis, starting at distance0, which is the edge of a conductive member, and extending to a distance10 μm from the edge of the conductive member, which is approximately acenter of the gap. The electric field across the gap is believed to beapproximately symmetric about the center of the gap; thus, only half ofthe gap was simulated. The graph in FIG. 10 shows the electric fieldstrength at points in the gap when the conductive members are exposed toa 2.45 GHz signal at various incident power levels. For example, at anincident power of about 1 watt/cm̂2, the electric field strength insidethe gap ranges from about 3.5×10̂5 volts per meter to about 6×10̂5 voltsper meter, as shown by line 1004. At an incident power of 0.1 watt/cm̂2,the electric field strength ranges from about 1×10̂5 volts per meter toabout 1.9×10̂5 volts per meter, as shown by line 1008. Both of theseincident power levels produce sufficient electric field strength toinitiate plasma in the gap. That is, both incident power levels exceed aplasma threshold of air 1010. Yet both of these incident power levelsremain safely below the dielectric breakdown threshold of air 1002.

Studies by others have shown that vanadium (IV) oxide (VO₂) can bestimulated to transition from an insulator phase to a metal phase by 7.1volts over a 3 micron gap, or a field strength of 2.4×10̂6 volts permeter, which is less than the field strength for a gap of a few micronsat incident power of 1 W/cm̂2. Accordingly, it is believed that thresholdpower for vanadium oxide can be lowered significantly below 1 W/cm̂2 witha smaller gap, even sub-micron sizes.

Different gap sizes may accommodate different incident power levelswithout exceeding the dielectric breakdown threshold of air 1002.Additionally, different gases may have different plasma thresholds anddielectric breakdown thresholds. Accordingly, a gap size and a gas maybe selected to provide protection for particular incident power levelsof particular frequencies of electromagnetic radiation.

FIG. 11 is a graph of simulated electric field characteristics acrosshalf of a gap of a discontinuous mesh according to a second particularembodiment. As in FIG. 10, only a half-gap is illustrated. The gapsimulated for FIG. 11 has a width of gap at 80 μm. Since the electricfield strength is believed to be symmetrical in the gap, the x-axisshows the distance from the edge of a conductive member at 0 to themidpoint of the gap at 40 μm. The graph in FIG. 11 also shows thedielectric breakdown threshold of air 1002 and the plasma threshold ofair 1010. The graph shows electric field strength for a 2.45 GHz signalat various incident power levels.

The electric field strength in the gap for a 1 watt/cm̂2 incident poweris shown by line 1108. Thus, for the 80 μm gap, 1 watt/cm̂2 incidentpower is sufficient to surpass the plasma threshold of air 1010 butremains below the dielectric breakdown threshold of air 1002. Theelectric field strength in the gap for a 5 watt/cm̂2 incident power isshown by line 1106, and the electric field strength in the gap for a 10watt/cm̂2 incident power is shown by line 1104. Both the 5 watt/cm̂2incident power and the 10 watt/cm̂2 incident power are sufficient tosurpass the plasma threshold of air 1010 but remain below the dielectricbreakdown threshold of air 1002. Thus, by widening the gap from the 20μm gap simulated in FIG. 10 to the 80 μm gap simulated in FIG. 11, ahigher incident power level signal can be blocked. For example, the 80μm gap can withstand at least a 10 watt/cm̂2 incident power level withoutreaching the dielectric breakdown threshold of air 1002.

FIG. 12 is a graph of simulated electric field characteristics acrosshalf of a gap of a discontinuous mesh according to a third particularembodiment. For FIG. 12, the gap was simulated as having a width of 20μm, with half of the gap shown in FIG. 12. FIG. 12 shows how a higherfrequency signal with a lower incident power level affects the electricfield in the gap. Specifically, FIG. 12 shows the electric field in thegap for various incident power levels of a 30.6 GHz signal, as comparedto the 2.45 GHz signal used for FIG. 10 with the same gap width. Theplasma threshold of air 1010 and the dielectric breakdown threshold ofair 1002 are also shown in FIG. 12.

The higher frequency signal used for FIG. 12 may provide better couplingacross the gap using less power. To illustrate, line 1206 shows theelectric field across the gap at a 1 mW/cm̂2 incident power level. Thus,using a 30.6 GHz signal, an incident power level as low as 1 mW/cm̂2 issufficient to generate a plasma in the gap. The line 1204 shows theelectric field across the gap at a 10 mW/cm̂2 incident power level.

While the simulations described above illustrate effects of frequency ofa received signal and gap width and power on generation of a plasma,another consideration is response time. That is, how long it takes forthe mesh to switch from an inactive state to an active state. Theswitching response time may be approximated by a time required for thephase change. For example, when the phase change material used is a gasthat transitions to a plasma, the switching response time isapproximately the plasma initiation time, e.g., how much time isrequired to initiate the plasma. The plasma is initiated when electronsof the gas in the gap become ionized. Thus, a time required for anelectron to achieve ionization energy in response to an electric fieldis an estimate of the plasma initiation time.

FIG. 13 is a graph of estimated turn on time of a protection deviceaccording to a particular embodiment. FIG. 13 graphs an approximation ofthe time required for an electron in an electric field to gain enoughenergy for ionization neglecting electron energy lost during inelasticcollisions with gas molecular species. This graph demonstrates that forvarious electric field strengths, the time required for an electron tobecome ionized is less than about two nanoseconds. Accordingly, the turnon response time for this particular embodiment is expected to be abouttwo nanoseconds or less. The solid-solid metal insulator phasetransition in vanadium dioxide has been estimated in some tests to takeapproximately 100 femtoseconds. Accordingly, embodiments that use asolid-solid metal insulator phase change material may have a responsetime that is less than one picoseconds, e.g., about 100 femtoseconds.

Various embodiments disclosed provide protection devices to protectelectronics. A protection device includes a discontinuous mesh that canact as a protective screen for communication systems and otherelectronic systems that may be susceptible to electromagnetic damage dueto high-power electromagnetic radiation. The discontinuous mesh may actas a nonlinear element that is substantially transparent toelectromagnetic radiation at low powers or particular frequencies andthat becomes substantially opaque or reflective to high-powerelectromagnetic radiation. The protection device may be passive in thatit reacts to switch from the transparent state to the opaque state inresponse to the incident electromagnetic radiation that is to beblocked. The protection device may also be actively controlled bytransmitting a signal having a desired modulation toward thediscontinuous mesh when it is desired to switch the discontinuous meshto a protection state. The protection device may include multiple layersof the discontinuous mesh to provide protection at different incidentpower levels.

The discontinuous mesh may act as an electromagnetic shutter to providepassive protection without requiring sensing systems or other complexcircuitry for switching. Characteristics of an incident signal (e.g.,the incident power level and frequency) may determine whether theincident signal is allowed to pass through the discontinuous mesh or isblocked by the discontinuous mesh.

Using active modulation, it is possible to illuminate the discontinuousmesh using a relatively high frequency, low power illumination signal inorder to activate the protection device. The frequency of theillumination signal may be approximately a resonant frequency of thediscontinuous mesh based on cell size (e.g., spacing of conductivemembers of the discontinuous mesh). Thus, the illumination signal mayhave a wavelength on an order of about two times the cell size. Sincethe discontinuous mesh may be designed for a working signal (e.g., asignal that is allowed to pass through) with a wavelength on an order ofabout twenty-five times the cell size there may be little interferencebetween the working signal and the illumination signal. Frequency of theillumination signal can also be chosen to be between harmonics ofoperating frequencies of an aperture associated with the protectiondevice to avoid unwanted coupling of the aperture. When activemodulation of the discontinuous mesh is used, polarization of theillumination signal may cause the screen to selectively block signalshaving a particular polarity. For example, depending on polarization ofthe illumination signal, either vertically or horizontally polarizedincoming signals may be blocked.

A unit cell size of the discontinuous mesh may be selected to improveperformance for particular incident signals. For example, the unit cellsize may be selected to be much smaller than a wavelength of theparticular incident signal to increase a reflection coefficient of thediscontinuous mesh. A gap width of the discontinuous mesh can beselected to mitigate a specific threshold level of incident power. Forexample, larger gaps may be used to mitigate higher incident powerlevels. Additionally, multiple discontinuous mesh layers with varyinggap widths can be used to mitigate a broader range of incident powerlevels. For example, two mesh layers may be used with a first layerhaving wider gaps than a second layer. The first layer may only turn onfor relatively high incident power levels. The second layer may beactivated for lower incident power levels, but may be overpowered by thehigher incident power levels. Additionally, when the first layer is ontop of the second layer, the second layer may be activated by “spillover” from the first layer, providing additional protection. That is,when a relatively high-power signal activates the first layer, a portionof the high-power signal may pass through the first layer. The portionof the high-power signal that passes through the first layer may besufficient to activate the second layer, enabling the second layer toprovide additional protection. Each layer may provide up to about 25decibels of attenuation and up to about 18 decibels of dynamic operatingrange of the incident power level.

The illustrations of the embodiments described herein are intended toprovide a general understanding of the structure of the variousembodiments. The illustrations are not intended to serve as a completedescription of all of the elements and features of apparatus and systemsthat utilize the structures or methods described herein. Many otherembodiments may be apparent to those of skill in the art upon reviewingthe disclosure. Other embodiments may be utilized and derived from thedisclosure, such that structural and logical substitutions and changesmay be made without departing from the scope of the disclosure. Forexample, method steps may be performed in a different order than isshown in the figures or one or more method steps may be omitted.Accordingly, the disclosure and the figures are to be regarded asillustrative rather than restrictive.

Moreover, although specific embodiments have been illustrated anddescribed herein, it should be appreciated that any subsequentarrangement designed to achieve the same or similar results may besubstituted for the specific embodiments shown. This disclosure isintended to cover any and all subsequent adaptations or variations ofvarious embodiments. Combinations of the above embodiments, and otherembodiments not specifically described herein, will be apparent to thoseof skill in the art upon reviewing the description.

The Abstract of the Disclosure is submitted with the understanding thatit will not be used to interpret or limit the scope or meaning of theclaims. In addition, in the foregoing Detailed Description, variousfeatures may be grouped together or described in a single embodiment forthe purpose of streamlining the disclosure. This disclosure is not to beinterpreted as reflecting an intention that the claimed embodimentsrequire more features than are expressly recited in each claim. Rather,as the following claims reflect, the claimed subject matter may bedirected to less than all of the features of any of the disclosedembodiments.

What is claimed is:
 1. A method, comprising: permitting a first signalhaving a first electromagnetic waveform to pass through an apparatus;and blocking a second signal having a second electromagnetic waveform atthe apparatus, wherein the second electromagnetic waveform is differentthan the first electromagnetic waveform; wherein the apparatuscomprises: a non-conductive substrate; a plurality of cells includingconductive members coupled to the non-conductive substrate, wherein theconductive members are arranged to form a first discontinuous mesh,wherein regions between the conductive members of the firstdiscontinuous mesh include a phase change material, wherein the phasechange material undergoes a phase transition from substantiallynon-conductive to substantially conductive.
 2. The method of claim 1,wherein the non-conductive substrate comprises a ceramic material, apolymer material, or a combination thereof.
 3. The method of claim 1,wherein dimensions of the conductive members are selected to permitpropagation of the first electromagnetic waveform and to blockpropagation of the second electromagnetic waveform.
 4. The method ofclaim 3, wherein each cell of the plurality of cells is approximatelysquare and has a length is approximately one-twenty-fifth of a firstwavelength of the first electromagnetic waveform.
 5. The method of claim4, wherein the length is approximately one-half of a second wavelengthof the second electromagnetic waveform.
 6. The method of claim 1,wherein the apparatus further comprises second conductive membersarranged to form a second discontinuous mesh, wherein the seconddiscontinuous mesh is layered over or under the first discontinuousmesh, wherein the conductive members of the first discontinuous mesh areseparated from each other by a first distance and the second conductivemembers of the second discontinuous mesh are separated from each otherby a second distance, and wherein the second distance is different fromthe first distance.
 7. The method of claim 1, wherein a gap is definedbetween the conductive members of the first discontinuous mesh atregions between the conductive members, and wherein the phase changematerial includes a gas that forms a plasma when the gas is excited byparticular electromagnetic waveforms.
 8. The method of claim 1, whereinthe phase change material includes vanadium (IV) oxide.
 9. A method,comprising: permitting a first signal having a first electromagneticwaveform to pass through an apparatus to an electronic device when theapparatus is in a first operational state; and selectively blocking asecond signal from passing to the electric device when the electronicdevice is in a second operational state, the second signal having asecond electromagnetic waveform that is different than the firstelectromagnetic waveform.
 10. The method of claim 9, wherein theapparatus comprises: a non-conductive substrate; a discontinuous mesh ofconductive members; and a phase change material disposed between theconductive members of the discontinuous mesh, wherein to transition fromthe first operational state to the second operational state the phasechange material undergoes a phase transition from substantiallynon-conductive to substantially conductive at least partially responsiveto the second electromagnetic waveform.
 11. The method of claim 9,further comprising transmitting a signal having the secondelectromagnetic waveform to cause the apparatus to transition to thesecond operational state.
 12. The method of claim 11, wherein a timerequired to switch from the first operational state to the secondoperational state is about 2 nanoseconds or less.
 13. The method ofclaim 12, wherein the time required to switch from the first operationalstate to the second operational state is less than one picosecond. 14.The method of claim 9, further comprising directing, by a secondelectronic device, a third signal having a third electromagneticwaveform toward the apparatus to cause a portion of the apparatus toundergo a phase transition to switch from the first operational state tothe second operational state.
 15. The method of claim 14, wherein thefirst electromagnetic waveform has a first polarization and furthercomprising selectively blocking a fourth signal having a secondpolarization responsive to the second electronic device directing thethird signal toward the apparatus.
 16. The method of claim 9, wherein atransition from the first operational state to the second operationalstate is a metal-insulator phase transition.
 17. A method, comprising:permitting a first signal having a first electromagnetic waveform topass through an apparatus; undergoing a phase transition at a portion ofthe apparatus responsive to a second signal having a secondelectromagnetic waveform; and blocking the second signal having thesecond electromagnetic waveform at the apparatus responsive toundergoing the phase transition, wherein the second electromagneticwaveform is different than the first electromagnetic waveform.
 18. Themethod of claim 17, wherein a wavelength of the second electromagneticwaveform is less than a first wavelength of the first electromagneticwaveform.
 19. The method of claim 17, wherein a power of the secondsignal at the apparatus is greater than a first power of the firstsignal at the apparatus.
 20. The method of claim 17, wherein the phasetransition is a metal-insulator phase transition.